Tribute to Professor Sia Nemat-Nasser

Abstract

A popular class of materials massively used at cryogenic temperatures comprises the stainless steels of different grades, such as 304, 304L, 316, 316Ti, 316L, 316LN etc. Such materials are metastable at extremely low temperatures, and usually undergo plastic strain induced phase transformation. In addition, these materials applied in the proximity of absolute zero exhibit the so-called discontinuous (intermittent, serrated) plastic flow (DPF). It consists in frequent, abrupt drops of stress against strain, characterized by increasing amplitude of the stress oscillations. Strong coupling between both phenomena: DPF and phase transformation is observed. Recent experiments performed by means of stainless steel samples tested in liquid helium (4.2 K) clearly indicate strong strain localization during DPF, in the form of shear bands propagating along the sample. However, as soon as the phase transformation process takes place, the motion of shear bands is hindered by formation of secondary phase. A physically based constitutive model developed in the present paper reflects coupling between the discontinuous plastic flow and the plastic strain induced phase transformation in the temperature range 0–T1. The model involves nonlinear mixed hardening, that occurs during the 2nd stage of each serration (stress–strain oscillation). The hardening is based on two mechanisms: interaction of dislocations with the inclusions of secondary phase, evolution of tangent stiffness operator due to changing proportions between the primary and the secondary phases. Nonlinear hardening strongly increases the stress level during each serration, which affects production of the internal lattice barriers, and the amount of the accumulated plastic strain. This, in turn, affects intensity of the phase transformation (full coupling). The constitutive model and its numerical version allow to reproduce the observed serrations, which is crucial for its application in the design of components operating at extremely low temperatures.